💡Anthropic Proves Fermat's Last Theorem in Lean with 13.4M Lines
Anthropic cracks Fermat's Last Theorem in 11 days with 13.4M lines
TL;DR
Anthropic used Lean to prove Fermat's Last Theorem in just 11 days, with a codebase of over 13.4 million lines. This formal proof could revolutionize formal verification in mathematics and beyond.
Anthropic has formalized a complete proof of Fermat's Last Theorem (FLT) in Lean, a theorem prover, in just 11 days. This achievement is significant for mathematicians and developers working on formal verification, as it demonstrates the power of automated theorem proving in complex mathematical problems. The proof, based on the Darmon–Diamond–Taylor exposition from 1995, uses the Langlands–Tunnell theorem and Ribet's level-lowering theorem. The codebase is over 13.4 million lines, taking nearly 20 times longer to compile than Lean's mathematics library. This formal proof could lead to more rigorous and automated verification of complex mathematical theories in the future.
Key Points
Anthropic's proof uses Lean, a theorem prover, to formalize Fermat's Last Theorem in 13.4 million lines of code.
The proof is based on the Darmon–Diamond–Taylor exposition from 1995, via the Langlands–Tunnell theorem and Ribet's level-lowering theorem.
The proof takes nearly 20 times longer to compile than Lean's mathematics library, highlighting the complexity of the formalization.
The author was given £1M to run their project over 5 years, aiming to train mathematics undergraduates in formalizing mathematics on computers.
The proof used 6 billion output tokens, which would cost $300,000 at the API price, demonstrating the computational resources required.
Why It Matters
If you're working on formal verification in mathematics or automated theorem proving, Anthropic's proof of Fermat's Last Theorem in Lean is a game changer. It shows the potential of automated tools to verify complex mathematical theories, reducing the risk of human error in formal proofs. The 13.4 million lines of code and the computational resources required also highlight the challenges and opportunities in this field.
Frequently Asked Questions
Why does this matter?
If you're working on formal verification in mathematics or automated theorem proving, Anthropic's proof of Fermat's Last Theorem in Lean is a game changer. It shows the potential of automated tools to verify complex mathematical theories, reducing the risk of human error in formal proofs. The 13.4 million lines of code and the computational resources required also highlight the challenges and opportunities in this field.
What happened?
Anthropic used Lean to prove Fermat's Last Theorem in just 11 days, with a codebase of over 13.4 million lines. This formal proof could revolutionize formal verification in mathematics and beyond.
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